Data-Driven Control of Large-Scale Networks with Formal Guarantees: A Small-Gain Free Approach

TL;DR

This paper introduces a data-driven divide-and-conquer method for controlling large-scale unknown networks, providing formal guarantees without relying on traditional small-gain conditions, and demonstrating linear sample complexity relative to the number of agents.

Contribution

It develops a novel data-driven compositional approach using symbolic models and bisimulation functions that reduces sample complexity and removes the need for known interconnection topology.

Findings

Reduces sample complexity from exponential to linear with respect to the number of agents.

Provides formal correctness guarantees for control strategies in unknown networks.

Applicable to networks with arbitrary and unknown interconnection topologies.

Abstract

This paper offers a data-driven divide-and-conquer strategy to analyze large-scale interconnected networks, characterized by both unknown mathematical models and interconnection topologies. Our data-driven scheme treats an unknown network as an interconnection of individual agents (a.k.a. subsystems) and aims at constructing their symbolic models, referred to as discrete-domain representations of unknown agents, by collecting data from their trajectories. The primary objective is to synthesize a control strategy that guarantees desired behaviors over an unknown network by employing local controllers, derived from symbolic models of individual agents. To achieve this, we leverage the concept of alternating sub-bisimulation function (ASBF) to capture the closeness between state trajectories of each unknown agent and its data-driven symbolic model. Under a newly developed data-driven compositional condition, we then establish an alternating bisimulation function (ABF) between an unknown network and its symbolic model, based on ASBFs of individual agents, while providing correctness guarantees. Despite the sample complexity in existing work being exponential with respect to the network size, we demonstrate that our divide-and-conquer strategy significantly reduces it to a linear scale with respect to the number of agents. We also showcase that our data-driven compositional condition does not necessitate the traditional small-gain condition, which demands precise knowledge of the interconnection topology for its fulfillment. We apply our data-driven findings to three benchmarks comprising unknown networks with an arbitrary, a-priori undefined number of agents and unknown interconnection topologies.